Practical Graphs
Maths: Edexcel IGCSE Higher, topic 3.3.5
Distance-Time Graphs
Distance-time graphs plot the distance travelled against the time. The gradient of a distance-time graph represents the speed (velocity) and direction of movement.
Distance-time graph
Gradient
- Steeper gradients mean faster speed and a negative gradient means the object is travelling back towards the start.
- If the graph is flat the object is stationary.
Calculating speed
- To calculate the speed from a distance-time graph, work out the distance travelled and the time taken for that section and calculate:
- Speed = distance ÷ time
Velocity-Time Graphs
Velocity-time graphs plot the velocity against the time.
Velocity
- Velocity is speed measured in a particular direction.
- Two objects travelling in opposite directions at a speed of 10km/h would have velocities of 10km/h and -10km/h.
Velocity-time graph
Gradient and area
- The gradient in a velocity-time graph represents acceleration.
- The area under the graph is the total distance travelled.
- When the graph is flat the velocity is constant.
- Steeper gradients mean stronger acceleration and negative slopes mean deceleration.
Conversion Graphs
Straight line graphs can be used to convert between different units of measurement.
Drawing conversion graphs
- Conversion graphs can be constructed from tables of two different units of the same measurement.
- The table above shows several distances measured in miles and the same distance measured in kilometres.
Drawing conversion graphs 2
- To draw the conversion graph for kilometres-miles, plot these values on a graph.
- Draw a straight line from the origin that connects all of the points.
Using conversion graphs
- To use the conversion graph, draw a line from the value you want to convert to the conversion line.
- Converting 7 miles gives approximately 11 km and vice versa.
Test yourself on Practical Graphs
What is the equation for speed?
What can we tell from the gradient of a distance-time graph?
If Usain Bolt travels 100 metres in 10 seconds, what is his average speed?
If Usain Bolt travels 50 metres in 4 seconds, what is his average speed?
If Usain Bolt travels 20 metres in 2.5 seconds, what is his average speed?